NC Milling
Simulating the process of numerically controlled (NC) milling is of fundamental importance in computer aided design (CAD) and computer aided manufacturing (CAM). During the simulation, a computer model of a workpiece is edited with a computer representation of an NC milling tool and a set of NC milling tool motions to simulate the milling process.
The workpiece model and tool representation can be visualized during the simulation to improve productivity, detect potential collisions between parts, such as the workpiece and the tool holder, and after the simulation to verify the final shape of the workpiece.
The final shape of the workpiece is affected by the selection of the tool, the tool motions and milling parameters. Instructions for controlling the motions are typically generated using the CAM system from a graphical representation of the desired final shape of the workpiece. The tool motions are typically implemented using numerical control programming language, also known as preparatory code or G-Codes, see, e.g., the RS274D and DIN 66025/ISO 6983 standards.
Swept Volumes
During milling, the tool moves relative to the workpiece according to a prescribed tool motion, referred to herein as a tool path. The tool path specifies the relative position, orientation, and other shape data of the tool with respect to the workpiece. In this disclosure, the milling is used as an example of the machining of the workpiece.
As the tool moves along the tool path, the tool carves out a “swept volume.” During the milling, as the tool moves along the tool path, a portion of the workpiece that is intersected by the swept volume is removed. This material removal can be modeled computationally as a constructive solid geometry (CSG) difference operation, in which the portion of the workpiece is removed from the workpiece using a CSG subtraction operation of the swept volume from the workpiece.
Although NC machining simulation is used as an example application, swept volumes have applications in many areas of science, engineering, entertainment, and computer graphics. Some specific applications include computer-aided design, freeform design, computer-based drawing, animation, solid modeling, robotics, manufacturing automation, and visualization to name but a few.
The swept volumes of simple shapes moving along simple paths can sometimes be represented analytically, as described in U.S. Pat. No. 4,833,617. However, those methods do not generalize to complex shapes and complex tool paths. Swept volumes can be represented and approximated by several geometric forms, such as polygonal methods, Z-buffer, depth pixel (dexel) method and voxel based representations. It is concluded that research in this field is limited by the difficulty of implementing complex mathematical formulations of swept volumes using software, and that computing the boundaries of swept volumes remains a challenging problem requiring better visualization tools and more accurate methods.
Models of polygonal shapes can be encoded in a spatial hierarchy for efficient editing via CSG operations. The accuracy of each of those polygonal methods is limited by the polygonal representation of the object model, see for example U.S. Pat. Nos. 6,862,560 and 6,993,461. Millions of polygons may be required to accurately represent the curved surface of a complex tool, especially if the radius of curvature is small. Methods that use binary voxels to represent swept volumes are described in U.S. Pat. No. 6,044,306 and “Octree-based Boundary Evaluation for General Sweeps”, Proceedings, TMCE, 2008, Erdim and Ilies. The accuracy of those methods is limited by the size of the smallest voxel used to represent the swept volumes. Thus, those methods may either have limited accuracy or have prohibitive processing times and memory requirements for generating high precision models of swept volumes, or both. In addition, methods that approximate the swept volume as a series of discrete time steps have limited precision between the discrete time steps, and are subject to aliasing artifacts.
Distance Fields
Distance fields are an effective representation for rendering and editing shapes, as described in U.S. Pat. Nos. 6,396,492, 6,724,393, 6,826,024, and 7,042,458. Distance fields are a form of implicit functions that represent an object. A distance field is a scalar field that gives a shortest distance to the surface of the object from any point in space. A point at which the distance field is zero is on the surface of the object. The set of points on the surface of the object collectively describe the boundary of the object, also known as the d=0 isosurface. The distance field of an object is positive for points inside the object, and a negative for points outside the object.
Adaptively sampled distance fields (ADFs) use detail-directed sampling to provide a much more space and time efficient representation of distance fields than is obtained using regularly sampled distance fields. ADFs store the distance field as a spatial hierarchy of cells. Each cell contains distance data and a reconstruction method for reconstructing a portion of the distance field associated with the cell. Distance data can include the value of the distance field, as well as the gradient and partial derivatives of the distance field. The distance field within a cell can be reconstructed only when needed to reduce memory and computational complexity.
Alternatively, the edited shape can be represented implicitly as a composite ADF (CADF). The CADF is generated to represent the object, where the CADF includes a set of cells arranged in the spatial hierarchy. Each cell in the CADF includes a subset of the set of geometric element distance field functions and a reconstruction method for combining the subset of geometric element distance field functions to reconstruct a composite distance field of a portion of the object represented by the cell. Each distance field in the subset of distance fields forms a part of the boundary of the object within the cell, called the composite boundary.
Tool Workpiece Engagement
During milling, as the tool moves along the tool path, the tool is in contact with the workpiece over a common surface which is called an “engagement surface.” As the tool moves relative to the workpiece, the tool carves out the swept volume. A portion of the workpiece that is intersected by the swept volume is removed, and called as “removed volume.” The workpiece that is updated by the removed volume is called an “in-process workpiece.” The engagement surface is the result of an intersection Boolean operation that occurs between the tool and the in-process workpiece.
To model the mechanics of the process, the dynamics, and to perform the machining process optimization accurately, it is necessary to have a precise geometric representation of the engagement surface. One of the inputs to the NC milling process simulation is the geometry of engagement surface between the tool and workpiece. The geometry of the engagement surface can have multiple disconnected sub-surfaces. The milling forces are applied between the tool and the workpiece through this engagement surface. Mechanistic modeling can be used to predict the milling forces, bending moment, spindle torque, spindle power, and tool defections from the instantaneous engagement surface and other parameters such as axial and radial depths, tool thickness, and errors of the surfaces due to tool deflections, parameters defining tool geometry, and milling parameters.
Various methods of determining the engagement surface are known. For example, boundary representation (B-rep) based milling simulation can analytically compute the engagement surface for simple milling tools, and 2.5 axis tool paths. See, Yip-Hoi and Huang: “Cutter/Workpiece Engagement Feature Extraction from Solid Models for End Milling,” ASME Journal of Manufacturing Science and Engineering, 2006, and Spence and Altintas: “A Solid Modeller Based Milling Process Simulation and Planning System,” Journal of Engineering for Industry, 1994. Both of those methods simulate the milling by a flat-end mill tool, and determine the engagement surface by a B-rep based solution. However, those methods are impractical for complex milling tools and tool paths due to the complexity of the computation and inconsistency of the results.
Several methods approximate the swept volume and engagement surface of the milling tool by polygonal shapes. Those methods include Aras and Yip-Hoi: “Geometric Modeling of Cutter/Workpiece Engagements in Three-Axis Milling Using Polyhedral Representations,” ASME Journal of Computing and Information Science in Engineering, 2008, and Yao: “Finding Cutter Engagement for Ball End Milling of Tessellated Free-Form Surfaces,” ASME IDETC/CIE 2005. The accuracy of polygonal-based methods is limited by the polygonal representation of the object model. However, millions of polygons may be required to accurately represent the curved surface and removed volume of a complex tool, especially if the radius of curvature is small. Thus, those methods either have limited accuracy or they have prohibitive processing times and memory requirements for calculating high precision tool workpiece intersection properties.
One of the fundamental difficulties has been the accurate and computationally efficient determination of the engagement surface along the tool path. The determination of the engagement surface is challenging due to complicated and changing tool workpiece intersection during NC milling. The geometric properties of the engagement surface comprise angle, area, orientation, curvature, shape, and etc., at any time.
Geometric Properties of Removed Volume
The simulation of the milling requires an accurate modeling of the material removed by the milling tool due to each tool movement. Accordingly, there is a need to determine the removed volume or an accurate geometric representation of the removed volume. Currently, CAD/CAM systems that generate tool path information employ the geometric and volumetric analysis to select parameters of a simulation and cutting. Average milling forces are assumed to be proportional to the material removal rate (MRR) at any particular time.
Volume computation of solid bodies is fundamental in many CSG applications. An overview of the importance and challenges in volume computation is described by Lee and Requicha in “Algorithms for computing the volume and other integral properties of solids. I. Known methods and open issues,” Communications of the ACM, 1982. Determining accurate moments and volumes of solids removed by milling tool along the tool path is difficult due to the presence of curved freeform surfaces. Therefore, the volumes are currently being computed by commercial software by first evaluating and tessellating the surfaces and computing the volumes of the tessellated objects as described in “ACIS Geometric Modeler: User Guide v20.0,” 2009, Spatial Corporation.
Another common method for volume calculation is converting the volume integrals to surface integrals by using a divergence theorem. That approach is described by Gonzalez-Ochoa, McCammon and Peters in “Computing moments of objects enclosed by piecewise polynomial surfaces,” Journal ACM Transactions on Graphics, 1998. Polyhedral approximations indicate that accurate evaluation of integral properties of curved objects via polyhedral approximations may require the use of polyhedral with a large number of faces. Numerical integration techniques are used to evaluate surface integrals of for a given polyhedral approximation. However, one of the main limitations is the level of tessellation in order to guarantee the accuracy of result.
Cellular approximations by using regular or octree subdivision are related to voxel-based representations, and these methods have accuracy and memory limited by the size of the smallest voxel used to represent the removed volume. For example, one method uses recursive subdivision surfaces as described by Peters and Nasri in “Computing Volumes of Solids Enclosed by Recursive Subdivision Surfaces,” EUROGRAPHICS 1997. That method computes the volume by estimating the volume of the local convex hull near extraordinary point. However the close-form representation of implicit, explicit or parametric forms is not always available, especially in NC milling case.
Milling Process Optimization
The time and cost of milling are key factors in this competitive industry. It is very important and difficult to choose suitable milling conditions to obtain high productivity due to complicated workpiece and geometry of cutter workpiece engagement, and the physics of the process. In complicated milling, it is critical, but often difficult, to select applicable cutting conditions to achieve high productivity while maintaining high quality of parts. Milling process optimization is the selection of machining parameters for a given process to achieve the maximum material removal rates within the process and machine constraints.
In addition computing the removed volume, other geometric properties of the milling process, such as mass, center of mass, surface area, moment of inertia, length, depth, width and thickness can also be computed to use for process analysis as described in U.S. Pat. Nos. 7,500,812 and 5,528,506. The moment of inertia of the removed volume is used for estimating the stresses applied by the milling tool to the workpiece, and later estimating the residual stresses left on the machined surface, spindle power and specific energy of cutting.
Conservative cutting conditions are most frequently used because there was a lack of accurate physical models and efficient optimization tools for the machining processes. The difficulty is most often the complicated surface geometry. Cutting forces acting between the tool and workpiece carry significant machining process information described in U.S. Pat. Nos. 7,101,126, 7,346,423 and 7,047,102. Since production engineers in industry have no scientific tools based on the mechanics of the free-form surface machining in most of the cases, the engineers cannot predict the cutting forces, therefore, there is no choice other than being conservative in the selection of the cutting conditions, such as feedrate value, spindle speed, depth and width of cut.
In planning of the NC machining process, the CAM software has to be conservative most of the time in selecting cutting conditions in order to prevent undesirable results, such as tool breakage, wear, dynamic run-out, deflection, over-cut or under-cut. In the past, the cutting conditions have been specified by an experienced machinist or selected from a machining database manual or handbook. Therefore, the traditional approaches result in a low productivity.
Feedrate Scheduling
The common practice in industry is to select the feedrate to improve productivity. High feedrate values can reduce the time of the machining but can adversely affect machining forces, tool deflections, surface form errors and wear on the tool and machine. The effectiveness of machining process is generally evaluated by the volume of the material being removed in a given time, often denoted as the material removal rate. The feedrate scheduling strategies can be classified into two groups: online and offline methods
The online methods, as described in “Feed rate optimization based on cutting force calculations in 3-axis milling of dies and molds with sculptured surfaces”, Int J Mach Tool Manufacturing 34, 1994, analyze the machining conditions through the measurement of tool deflection, cutting forces/torque, vibrations, chatter, temperature, spindle power, motor current. Machining parameters are consistently varied, based on the continual measurement of cutting zone parameters with the help of sensors. However, the sensors may not sufficiently accurate to work in adverse conditions.
As opposed to the online methods, the offline methods are flexible and versatile. The machining conditions can be obtained by means of a computer simulation. The models in “A solid model-based milling process simulation and optimization system integrated with CAD/CAM”, Journal of Materials Processing Technology, 2003 and “Solid modeling for optimizing metal removal of three-dimensional NC end milling”, Journal of Manufacturing Systems, 1988 used in offline method can be classified extensively into several categories.
The first category uses volumetric models where the feedrate is proportional to either an average material removal rate (MRR). The power required to cut the material is proportion to the volumetric removal rate. It is assumed that the average cutting forces are proportional to the MRR. These kinds of volumetric approaches given in “The implementation of optimum MRR on digital PC-based lathe system”, Int Journal Adv. Manufacturing Technology, 2007 predict average forces, not the peak or the instantaneous forces. The feedrate scheduling is performed by using geometrical information such as chip cross section, chip volume and engagement angles. The swept volume for each NC block segment is the average MRR, and the average MRR may be very different from the peak MRR.
The second category uses a rule based model that implements the principles of artificial intelligence techniques, genetic algorithms, response surface, empirical relations between force and process conditions. Another method uses a physical model of the interaction between the tool and workpiece. That physical model predicts the cutting load by using a force model and adjusts the parameters accordingly. The force models are generally accurate, but difficult too difficult to be determines for general cases.
Some offline feedrate scheduling strategy arranges the constant feedrate values in order to increase the resultant force to the desired reference value using a linear relation between the feedrate and the reference limiting cutting force. These feedrate scheduling methods adjust the feedrate to limit force, as described in “U.S. Pat. Nos. 7,050,883” and “U.S. patents No. 20050113963,” however, those methods are still insufficient for determining the best optimized feedrate values.
Thus there is a need for a method for scheduling the feedrate values to improve the productivity and cycle times.